As the temperature drop, so does your child’s tolerance for being cooped up indoors. But with sleet rain and the flu bug at large, you can’t always let them frolic outdoors.

Luckily, there are lots of places to amuse the young and restless.

Here are four that are guaranteed to put smiles on the faces of kids of all ages.

Right in the heart of the revamped Times Square is Broadway City – an arcade “city” features landmarks like the Brooklyn Bridge (which you can walk over), the head of the Statue of Liberty and a remarkably realistic replica of an old-time (circa 1920s) subway station, complete with greenish copper poles and vintage posters

So much for the past.

The arcade’s three floors are designed in a distinctly New Age way, with circular holes at random points in the floor, allowing patrons to witness gaming on all three tiers. As for the machines themselves, they date from the early ’80s on, with old-school Ms. Pac Man awaiting the nostalgic on the arcade’s ground floor.

The high-tech new games feature enough simulators to stimulate the most jaded kids in the city. You can ride a roller coaster, take the wheel of a Ferrari, and play drums in your favorite band – all without leaving 42nd street.

How much: Video games cost between 50 cents and $1.50 each, the simulators start at $5.

Information: Call 212 997-9797.

Since the Chelsea Piers opened in 1994, it’s become an indoor mecca for city jocks of every age. And there’s a lot here for kids. For starters, there’s a sports camp each Saturday through late April, each session running for one month.

And then there’s the field house, which is open every day through winter. The field house is divided into two sections, with gymnastics and rock climbing on one side, and soccer and basketball on the other. Gymnastic areas have foam pits and the 28-foot rock climbing wall open to kids age 4 and up. There’s also indoor soccer – a rarity in the city and suburbs too, for that matter – and six basketball courts.

Also indoors, just behind the field house, are batting cages where the kids can make like Mike Piazza. And just down the way, at Pier 59, is a four-level driving range, overlooking the river. Junior Open Tee time is Tuesdays from 3-5 p.m., when $10 lets kids drive all the golf balls they want. Clubs come in all sizes – so even the youngest Tiger Woods wannabes can get into the swing of things.

Where: Piers 59-62, at 23rd Street and the West Side Highway

When: 9 a.m.- 10 p.m. daily. Field house times vary, so call for specific sports hours.

How Much: Gymnastics and rock climbing cost $17 per participant, Basketball courts and soccer fields are $7 per hour while $1 gets you 10 pitches in the batting cage.

Information: (212) 336-6500.

Video games, miniature golf … and an elephant carousel. You’ll find all three and more at Sportsworld a 57,000- square-foot recreation center featuring everything from skee-ball to laser tag.

Along with video games and simulators are bumper cars and “bowlingo” (which is just like bowling except with much smaller pins). And laser-tag fans will find a 4,500-square-foot black-lit arena that’s just for them.

When the kids get hungry, let them refuel at the snack bar, which sells $2 hot dogs, $1.70 slices of pizza and more. And the sportscenter’s picnic benches are strategically placed, so the kids can watch all the action while they chow down.

How much: Tokens are 25 cents, and video games cost 1-4 tokens. Laser tag is $7 per person, and the simulator motion theater (including a choice of 10 different rides) costs $5 a piece.

Information: (201) 262-1717

Most everyone has been to the top of the Empire State Building. But not everyone knows about the skyscraper’s second-floor skyride.

Join James “Scotty”Doohan of “Star Trek” fame as he narrates a simulated tour of New York City. You’ll fly above the Brooklyn Bridge, glide by the Statue of Liberty, and literally crash into F.A.O. Schwarz.

The seats move along with the on-screen action. For the 20-minute duration of the ride, you actually feel as if you’re airborne, dodging in and out of New York City’s biggest landmarks without having your ears pop.

One warning: No children under 5 are permitted, and there’s a 36 inch minimum height requirement.

Where: 34th Street and Fifth Avenue, 2nd floor.

When: 10 a.m.- 10 p.m.

How much: $11.50 for adults, and $8.50 for kids. A combo package, including Skyride and a trip to the top of the Empire State Building, is $15 for adults and $10 for kids.